1. Combinatorial Analysis: Principle of addition and multiplication, permutations, arrangements, and combinations.
2. Probability Theory: Sample space and events, axiomatic foundation of probability theory, laws of probability.
   Conditional probability, independent events, law of total probability, Bayes’ theorem.
3. Random Variables: Basic concepts, probability mass functions and probability density functions, cumulative distribution function, mean value, variance and standard deviation, basic discrete and continuous probability distributions.
4. Descriptive Statistics: Frequency distributions and graphical representations, numerical descriptive measures of data.
5. Statistical Inference: Point estimators. Confidence intervals for means, variances, and proportions.
   Hypothesis testing for means and variances. Correlation and regression.

Learning Outcomes

The course constitutes a fundamental introductory course to the concepts of Probability and Statistics.
Specifically, the course content aims to familiarize students with the basic principles of Combinatorial Analysis, Probability Theory, random variables, probability and distribution functions, descriptive measures of distributions, and standard probability distributions.

The syllabus also includes a detailed treatment of Descriptive Statistics, confidence intervals, and hypothesis testing, as well as an introduction to the concepts of correlation and regression.

Upon successful completion of the course, the student will be able to:

• Effectively apply the fundamental laws of Probability.
• Use appropriate probability distributions to compute probabilities.
• Analyze data using tools of Descriptive Statistics.
• Apply confidence intervals and hypothesis testing in decision-making processes.